From a point PPP outside a circle with center OOO, tangents PAPAPA and PBPBPB are drawn to the circle. The line segment formed by joining the points AAA and BBB intersect the line segment OPOPOP at MMM. Find the measure of ∠AMP∠AMP∠AMP.
Answer:
90∘90∘90∘
- Given:
PAPAPA and PBPBPB are the tangents to the circle from an external point PPP.
To find:
The measure of ∠AMP∠AMP∠AMP. - In △MAP△MAP△MAP and △MBP△MBP△MBP, we have [Math Processing Error] Thus, △MAP≅△MBP [By SAS-congruence]△MAP≅△MBP [By SAS-congruence]
- As the corresponding parts of congruent triangles are equal, MA=MBMA=MB and ∠AMP=∠BMP.∠AMP=∠BMP.
Also, [Math Processing Error] - Therefore, the measure of ∠AMP∠AMP is 90∘90∘.